Hi @finch and welcome to the forum!
First question: why do you think your device has a maximum current of 3 mA? The “maximum” current depends upon measurement bandwidth. If I look at the plot, I estimate an average current of about 3 mA during that activity window (1.5 mA over the entire plot with roughly half being the activity window). If you were to look at this same activity with a 1 kHz sampling rate, which you can do using downsampling, you won’t see this peaking as much.
Now, we have had some infrequent reports of RF energy coupling into the JS110, either conducted or radiated. However, these have been with much higher power radios, like +30 dBm that were poorly located. In one case, the wires connecting the device to the Joulescope were accidentally part of the antenna. In another case, the JS110 enclosure became part of the antenna. The Joulescope JS110 measurement range is asymmetric, and it measures more positive than negative. Extreme RF signals get rectified resulting in a DC bias.
You can do a simple test to see if this is the case. First, locate the device further away from the JS110 by using longer wires, say 2 feet. Ensure that you twist the OUT+ and OUT- wires together to minimize the loop area and RF pickup. Do you measure the same values? If so, the Joulescope measurements are likely correct.
The next step to build confidence is to use another piece of equipment to confirm the measurements. Do you have access to an oscilloscope? Oscilloscopes are usually earth-ground referenced, which can complicate things. Assuming you can float your system or the oscilloscope, you can measure the voltage across your Joulescope’s IN+ to OUT+. You will expect to see about 15 mV (12 mA * (1.11 + 0.015) Ω). If you can disconnect your target device from everything and power using a battery, then you don’t need to worry. If you need help otherwise, let me know!